Solve for $x$ and $y$ using elimination. ${3x+3y = 30}$ ${-2x-3y = -28}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {3x+3y = 30}\thinspace$ to find $y$ ${3}{(2)}{ + 3y = 30}$ $6+3y = 30$ $6{-6} + 3y = 30{-6}$ $3y = 24$ $\dfrac{3y}{{3}} = \dfrac{24}{{3}}$ ${y = 8}$ You can also plug ${x = 2}$ into $\thinspace {-2x-3y = -28}\thinspace$ and get the same answer for $y$ : ${-2}{(2)}{ - 3y = -28}$ ${y = 8}$